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Question

Draw the graph of |x|+|y|+|x+y|=1.

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Solution

We know that,
|x|={xx0xx<0
|y|={yy0yy<0
|x+y|=⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪xyx<0,y<0x+yx<0,y0xyx0,y<0x+yx0,y0
So, we can write |x|+|y|+|x+y|=1
as ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪x+y+x+y=1x+yx+y=1xy+xy=1xyxy=1=⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪x+y=12yx=12xy=12x+y=12.

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